Medical imaging using advanced three-dimensional (3-D) or four-dimensional (e.g., 3-D plus time dimension) modalities, such as Computed Tomography (CT), Single Photon Emission CT (SPECT), and Magnetic Resonance (MR) has become an important contributor to healthcare, providing valuable information during the screening, diagnostic, treatment planning, clinical monitoring, and/or prognostication phases. There is an increasing need for representation of objects of interest (OOIs) detected by imaging specialists within the produced data sets as display extractions (e.g., colored 3-D renderings) or as quantitative elements (e.g., histograms of changing volume or mass) for improved understanding of anatomic relationships or disease extent by clinicians applying the insights to decision making about patient care. To date, techniques directed at these goals have been largely modality-specific or industry-specific, which typically precludes integrative use across imaging applications.
Radial Basis Functions (RBFs) have been applied to the interpolation of scattered data in various studies. In some studies, RBF-based multilevel approaches were used for the interpolation of scattered height data. More recently, a technique was introduced where the scattered data is interpolated with locally and globally supported basis functions in a hierarchical fashion for 3-D model reconstruction applications. Using constraining scattered data, this approach sought an implicit function separating the inside of the object from its outside using function valued RBFs; this approach produced impressive results when only a few hundred model mesh points and their normal directions were provided. Extending similar concepts to medicine, for example, two different studies used novel formulation of RBFs for the delineation of body part borders. In the first of the two studies, RBFs were fitted to depth maps of skull surfaces in CT image data in order to smoothly interpolate the surface of the skull across regions containing defects; in so doing, this study defined a model for future investigations as it: (1) applied RBFs in a medical setting (i.e., cranioplasty procedure), and (2) compared Thin Plate Splines (TPSs) and Linear Radial Bases (LRBs). In the approach used with the second study, the shapes defined in N dimensions by multiple constraining “seeds”—or reference points—were transformed, creating an (N+1)-dimensional ((N+1)-D) shape; briefly, for generating an (N+1)-D surface: (1) scattered boundary/normal constraints were delineated in multiple N-dimensional (N-D) images, and (2) a stack of N-D constraints underwent variational interpolation to create a single implicit function defining an (N+1)-D shape. This approach can be applied to a variety of topologies. However, when segmenting 3-D images, many constraining seeds, which include the boundary and normal for each seed position, will likely need to be provided for multiple selected 2-D cross-sections; this can be a very labor-intensive process.